Write the following equations in factored form. Remember to common factor first

Question

(if possible).
𝑦 = 2𝑥power 2 + 3𝑥 − 2

Answer 1

First, let's see if we can common factor anything. The coefficients of the quadratic term and the linear term are both even, so we can factor out a 2:

𝑦 = 2(𝑥power 2 + (3/2)𝑥 − 1)

Now we need to factor the quadratic term inside the parentheses. We can use either factoring by grouping or the quadratic formula. For this example, we'll use factoring by grouping:

𝑦 = 2(𝑥 − 1/2)(𝑥 + 2)

So the factored form of the equation 𝑦 = 2𝑥power 2 + 3𝑥 − 2 is 𝑦 = 2(𝑥 − 1/2)(𝑥 + 2).